In the Internet era, leakage of personal information becomes an important issue. When wireless communication techniques such as RFID (radio frequency identification) are used in transaction, there is a risk that the personal information in a smart card may be stolen either during the wireless transaction process or by an unauthorized reader.
A conventional anonymous authentication method employs a private authentication system in identification and/or authentication of RFID chips, and personal information is no longer provided during communication between the RFID chips and readers. Instead, the RFID chips encrypt non-specific data that are to be provided to the readers for enhancing safety. In such conventional method, each RFID chip corresponds to one distinct key, so when a large number (e.g. 1,000,000) of RFID chips use the authentication system, the back-end server system has to perform trials of decryption using a corresponding number (e.g., 1,000,000) of keys one by one to acquire a correct key that can successfully decrypt the encrypted data. As a result, trials of decryption and time required for acquiring the correct key may linearly increase with increase of the number of RFID chips, leading to high cost and inefficiency.